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forsale [732]
3 years ago
14

Solve the system. 2x+y = 3 -2y = 14 - 6x

Mathematics
2 answers:
Elena L [17]3 years ago
7 0

For this case we have the following system of equations:

2x + y = 3\\-2y = 14-6x

We clear "y" from the second equation:

y = \frac {14} {- 2} - \frac {6x} {- 2}\\y = -7 + 3x

We substitute in the first equation:

2x + (- 7 + 3x) = 3\\2x-7 + 3x = 3\\5x-7 = 3\\5x = 3 + 7\\5x = 10\\x = \frac {10} {5}\\x = 2

So:

y = -7 + 3x\\y = -7 + 3 (2)\\y = -7 + 6\\y = -1

The solution is: (x, y) :( 2, -1)

Answer:

(x, y) :( 2, -1)

bezimeni [28]3 years ago
5 0

Answer:

The solution is: (2, -1)

Step-by-step explanation:

First we rewrite the second system equation

-2y = 14 - 6x   →   6x-2y=14

Now we have the following system of equations:

2x+y = 3

6x-2y=14

To solve the system multiply the first equation by -3 and add it to the second equation

-6x+-3y = -9

6x-2y=14

--------------------------------------

0-5y=5

y=-1

Now we substitute the value of y in the first equation and solve for x

2x-1 = 3

2x= 4

x= 2

The solution is: (2, -1)

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This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where 
m=slope of line
(x0,y0) is a point through which the line passes.

We know that the line passes through A(3,-6), B(1,2)

All options have a slope of -4, so that should not be a problem.  In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.

So we can check which line passes through which point:

a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3)  means that line passes through A(3,-6) => ok

b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
   ****** this equation is not the line passing through A & B *****

c. y=-4x+6  subtract 2 from both sides (to make the y-coordinate 2)
   y-2 = -4x+4, rearrange
   y-2 = -4(x-1)  
   which means that it passes through B(1,2), so ok

d. y-2=-4(x-1)
   this is the same as the previous equation, so it passes through B(1,2), 
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Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
   
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3 years ago
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